Zobrazeno 1 - 10
of 98
pro vyhledávání: '"P., Wakhare"'
Autor:
Wakhare, Tanay
We embark on a systematic study of the $(k+1)$-th derivative of $x^{k-r}H(x^r)$, where $H(x):=-x\log x-(1-x)\log(1-x)$ is the binary entropy and $k>r\geq 1$ are integers. Our motivation is the conjectural entropy inequality $\alpha_k H(x^k)\geq x^{k-
Externí odkaz:
http://arxiv.org/abs/2312.14743
Autor:
Melamed, Rimon, McCabe, Lucas H., Wakhare, Tanay, Kim, Yejin, Huang, H. Howie, Boix-Adsera, Enric
We discover that many natural-language prompts can be replaced by corresponding prompts that are unintelligible to humans but that provably elicit similar behavior in language models. We call these prompts "evil twins" because they are obfuscated and
Externí odkaz:
http://arxiv.org/abs/2311.07064
Autor:
Wakhare, T., Vignat, C.
An unpublished identity of Gosper restates a hypergeometric identity for odd zeta values in terms of an infinite product of matrices. We show that this correspondence runs much deeper, and show that many examples of WZ-accelerated series for zeta val
Externí odkaz:
http://arxiv.org/abs/2301.00298
Dirichlet Series Under Standard Convolutions: Variations on Ramanujan's Identity for Odd Zeta Values
Inspired by a famous identity of Ramanujan, we propose a general formula linearizing the convolution of Dirichlet series as the sum of Dirichlet series with modified weights; its specialization produces new identities and recovers several identities
Externí odkaz:
http://arxiv.org/abs/2107.06457
Autor:
Cioabă, Sebastian M., Ostuni, Anthony, Park, Davin, Potluri, Sriya, Wakhare, Tanay, Wong, Wiseley
Liu, Hong, Gu, and Lai proved if the second largest eigenvalue of the adjacency matrix of graph $G$ with minimum degree $\delta \ge 2m+2 \ge 4$ satisfies $\lambda_2(G) < \delta - \frac{2m+1}{\delta+1}$, then $G$ contains at least $m+1$ edge-disjoint
Externí odkaz:
http://arxiv.org/abs/2104.01665
Autor:
Park, Davin, Ostuni, Anthony, Hayes, Nathan, Banerjee, Amartya, Wakhare, Tanay, Wong, Wiseley, Cioabă, Sebastian
The \textit{toughness} $t(G)$ of a graph $G$ is a measure of its connectivity that is closely related to Hamiltonicity. Brouwer proved the lower bound $t(G) > \ell / \lambda - 2$ on the toughness of any connected $\ell$-regular graph, where $ \lambda
Externí odkaz:
http://arxiv.org/abs/2008.08183
Autor:
Wakhare, Tanay
Dan Romik recently considered the Taylor coefficients of the Jacobi theta function around the complex multiplication point $i$. He then conjectured that the Taylor coefficients $d(n)$ either vanish or are periodic modulo any prime ${p}$; this was pro
Externí odkaz:
http://arxiv.org/abs/1909.01485
Autor:
Wakhare, Tanay, Vignat, Christophe
We extend some results recently obtained by Dan Romik about the Taylor coefficients of the theta function $\theta_{3}\left(1\right)$ to the case $\theta_{3}\left(q\right)$ of an arbitrary value of the elliptic modulus $k.$ These results are obtained
Externí odkaz:
http://arxiv.org/abs/1909.01508
Autor:
Wakhare, Tanay, Johnson, Charles R.
We prove the sufficiency of the Linear Superposition Principle for linear trees, which characterizes the spectra achievable by a real symmetric matrix whose underlying graph is a linear tree. The necessity was previously proven in 2014. This is the m
Externí odkaz:
http://arxiv.org/abs/1906.06257
We introduce a symbolic representation of $r$-fold harmonic sums at negative indices. This representation allows us to recover and extend some recent results by Duchamp et al., such as recurrence relations and generating functions for these sums. Thi
Externí odkaz:
http://arxiv.org/abs/1903.07215